2018 AMC 10A Problem 24

Triangle ABC with AB=50 and AC=10 has area 120. Let D be the midpoint of \overline{AB}, and let E be the midpoint of \overline{AC}. The angle bisector of \angle BAC intersects \overline{DE} and \overline{BC} at F and G, respectively. What is the area of quadrilateral FDBG?

\textbf{(A) }60 \qquad \textbf{(B) }65 \qquad \textbf{(C) }70 \qquad \textbf{(D) }75 \qquad \textbf{(E) }80 \qquad

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.